Lets consult to the trigonometry exact value table attached.
arccsc sqrt(2)
csc(t) = sqrt(2)
we know that:
csc theta = 1/sin(theta)
where theta = angle
so,
1 / sin(theta) = sqrt 2
sin(theta) = sqrt 2 / 2
Theta = pi/4 or 45 degrees
or
Theta = 3 pi/4 or 135 degrees
